Follow strictly the Five Steps in Hypothesis Testing (copy and attach this to your solutions)

1. State the null and alternative hypothesis

2. Select the level of significance

3. Select the test statistic

4. Formulate the decision rule

5. Make a decision and interpret the results.

The Canadian company Encircled Ltd makes thoughtfully-designed, versatile capsule wardrobe essentials. All fabrics are thoughtfully chosen to meet the company's high standards in wearability and sustainability. The owner wants to determine whether the sales of the Evolve tops increases during the summer months only (June - August). In particular, the mean number of Evolve tops per week in 2020 is 37. Following is a sample of 8 weeks during the months of June, July and August 2020.

35

42

38

45

45

41

35

38

Required:

(a) At 0.10 significant level, can the owner conclude that the mean number of Evolve tops sold during the summer season is larger? (11 marks)

(b) In complete sentences, state the Type I and Type II errors in the case of Encircled. (2 marks)

(c) Should the owner increase her capacity and produces more Evolve tops for the summer season? Why or why not? What is the risk? (2 marks)